“Optimization” generally means to conduct the best decision under a certain condition or to select the best one from a number of alternatives. A problem of such optimization is put into a following formula as a mathematical model.
“Find a value of a variable with which a function showing the scale of desirableness called an objective function becomes the maximum or minimum, under a given limited condition.”
Note that there are a plurality of variables in general, so that those are expressed with n-order vector, and the optimization problem is expressed as in a following expression (1).Objective function: f(x)→minimumLimited condition: xεS  Expression (1)
In Expression (1), the objective function f is a real-valued function defined on an appropriate aggregate including S. Further, S shows an aggregate of values the variable x can take in this optimization problem.
Furthermore, the optimization described above is conducted on the Internet that is a communication network. For example, with the TCP protocol, there is a mechanism called a slow start for controlling the transmission amount of the communication traffic to optimum so as to avoid expansion of traffic congestion on the network. Further, back pressure congestion control (a method which transmits a collision signal to the transmission side to hold transmission of a station on a segment) in the Ethernet (registered trademark), a method using “PAUSE command” which performs flow control in a MAC control protocol, and the like have been put into practical use.
Other than those described above, an optimization method for transferring only the traffic for a certain special application as fast as possible on the communication network, etc., is employed on a P2P (Peer-to-Peer) network and the like.
For a long period of time, researchers of the Internet traffic had thought that the traffic exhibits random variations. However, in 1994, it was reported by Leland and others that there is a self-similarity in the traffic. Ever since, there have been a great number of researches done on the behaviors of the Internet traffic. For example, Fukuda and Takayasu of NTT and others have shown that cumulative probability density distribution of a communication traffic variation shows a phase transition phenomenon, and appears as a power-law distribution with an exponent of −1 when the origin at a critical point is taken as 10 to the power of 0 (i.e., “1”). Some observation data are presented to show that the distribution at the critical point becomes the power law with an exponent of −1 in the phase transition phenomenon of the cumulative probability density distribution.
Further, a group of J. C. Doyle, S. H. Low and others as well as Fukuda and others have reported that the main factor of such traffic behavior is due to the feedback control in TCP and the Ethernet and the mechanism itself of the buffer function (or delay) in the feedback (see Non-Patent Document 1-Non-Patent Document 3). Further, it has been confirmed that the traffic efficiency becomes the maximum at the critical point in the phase transition of the system that has such mechanism (see Non-Patent Document 4).
In the meantime, it is known that there is a possibility that the power law is not applied in the traffic of each application unlike the case of the total traffic and that the aggregate traffic thereof regarding P2P and Web that are the currently dominant traffics exhibit the power law. However, these are only recognized as the phenomena, and there is no case of example where the phenomena are used in the evaluation of the communication traffic optimization technique.
Including those presented as the examples above, basically the effectiveness of the communication traffic optimization control techniques is only confirmed by a simple network model in simulations. Thus, whether or not the optimization techniques are really optimum (i.e., whether or not the objective function is the minimum or maximum) cannot be grasped on the actual Internet and other communication networks.
Non-Patent Document 1: John C. Doyle, etc., “Robustness and the Internet: Theoretical Foundations” Mar. 5, 2002.
Non-Patent Document 2: Misako Takayasu, etc., “Dynamic phase transition observed in the Internet traffic flow”, Sep. 21, 1999.
Non-Patent Document 3: Kensuke Fukuda, etc., “Origin of critical behavior in Ethernet traffic” Jul. 21, 2000.
Non-Patent Document 4: Kensuke Fukuda, etc., “A case of self-similarity in TCP traffic”, Mar. 15, 2005.